Difference between revisions of "Faber F1"

From specialfunctionswiki
Jump to: navigation, search
Line 29: Line 29:
 
=References=
 
=References=
 
[https://pure.ltu.se/ws/files/30923977/LTU-EX-03320-SE.pdf]
 
[https://pure.ltu.se/ws/files/30923977/LTU-EX-03320-SE.pdf]
 +
 +
[[Category:SpecialFunction]]

Revision as of 18:34, 24 May 2016

The Faber function $F_1$ is defined by $$F_1(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{10^k} \displaystyle\inf_{m \in \mathbb{Z}} \left|2^{k!} x -m \right|.$$

Properties

Theorem: The Faber function $F_1$ is continuous.

Proof:

Theorem: The Faber function $F_1$ is nowhere differentiable.

Proof:


See Also

Faber function F2

References

[1]